I think the relation between Zed and Akali is more of a possible future aspect more than something of the past. Zed despises the Kinkou because Shen always beat him and when he learned forbidden Shadow Arts he was exiled. Yet Akali AND her mother were trained in the same knowledge that Zed was told is forbidden (Or so I assume since Akali's mother had the title Fist of Shadow and passed it onto Akali, and her passive is Twin Disciplines).

Possibly the interaction between them is how Zed is Master of Shadows but Akali has the full story to balance, and is as such still a Kinkou but clearly a user of the forbidden shadow arts. It of course would be humorous enough to see another love/hate relationship between them like Garen/Kat but I think it'll have more to do with Zed and the Kinkou and Balance and such if they ever move the lore forward and Swain ends up destroying Valoran as they know it.

It of course would be humorous enough to see another love/hate relationship between them like Garen/Kat.

I don't think it would be as much of a love/hate thing as Akali wanting to kill Zed. She is supposed to be Pruning the Tree. He may be an enemy of all the Kinkou, but his elimination is her duty alone. She has a penchant for violent punishments, so I'm sure she wants his head as soon as possible.

The judgement itself is the Eye of Twilight's decision, so the final battle between Akali and Zed will probably happen when Shen makes the call.